Compression Of A Three-Dimensional Modeled Object

ABSTRACT

It is proposed a computer-implemented method for compressing a three-dimensional modeled object. The method comprises: providing a mesh of the three-dimensional modeled object; parameterizing (u,v) the mesh in a two-dimensional plane, the parameterization of the mesh resulting in a set of vertices having two-dimensional coordinates; providing a grid on the two-dimensional plane; and modifying the two-dimensional coordinates of each vertex by assigning one vertex to one intersection of the grid. Such compression method is lossless, completely reversible, suitable to efficiently reduce the storage size of a CAD file.

RELATED APPLICATION(S)

This application claims priority under 35 U.S.C. §119 or 365 to Europe,Application No. 13306101.0, filed Jul. 30, 2013. The entire teachings ofthe above application(s) are incorporated herein by reference.

FIELD OF THE INVENTION

The invention relates to the field of computer programs and systems, andmore specifically to a method, system and program forcompressing/uncompressing a three-dimensional modeled.

BACKGROUND OF THE INVENTION

A number of systems and programs are offered on the market for thedesign, the engineering and the manufacturing of objects. CAD is anacronym for Computer-Aided Design, e.g. it relates to software solutionsfor designing an object. CAE is an acronym for Computer-AidedEngineering, e.g. it relates to software solutions for simulating thephysical behavior of a future product. CAM is an acronym forComputer-Aided Manufacturing, e.g. it relates to software solutions fordefining manufacturing processes and operations. In such computer-aideddesign systems, the graphical user interface plays an important role asregards the efficiency of the technique. These techniques may beembedded within Product Lifecycle Management (PLM) systems. PLM refersto a business strategy that helps companies to share product data, applycommon processes, and leverage corporate knowledge for the developmentof products from conception to the end of their life, across the conceptof extended enterprise.

The PLM solutions provided by Dassault Systemes (under the trademarksCATIA, ENOVIA and DELMIA) provide an Engineering Hub, which organizesproduct engineering knowledge, a Manufacturing Hub, which managesmanufacturing engineering knowledge, and an Enterprise Hub which enablesenterprise integrations and connections into both the Engineering andManufacturing Hubs. All together the system delivers an open objectmodel linking products, processes, resources to enable dynamic,knowledge-based product creation and decision support that drivesoptimized product definition, manufacturing preparation, production andservice.

In the field of computer graphics, the surface of a 3D object is oftenrepresented by a collection of triangles (or more generally by acollection of polygons) in a 3D space. These polygons are connectingvertices which hold different properties. Among these differentproperties each vertex has at least a definite position in space (x, yand z). This kind of representation is called a polygonal mesh. It isalso called a triangular mesh if the representation only containstriangles. A polygonal mesh can be divided in two types of data: (i)geometry data comprise the whole set of positions and other propertiesfor each vertex, and (ii) connectivity data comprise the indices of thevertices joined by each polygon.

3D objects and surface geometries of 3D objects can be stored on apersistent support in a straightforward implementation, i.e. withoutcompression. This straightforward storage (i.e. without compression) isnotably used in CATIA and in other CAD software. With such a storing,the storing is lossless. Indeed, the data defining the model is notmodified before storing, and there can therefore not be any loss ofdata. The storing is also stable. Indeed, the data defining the model isnot to be transformed when the model is reopened, because the data isnot compressed. However, such a method fails to optimize the storagesize of a CAD model.

To this aims, several compression schemes have been developed. Remeshingis one of the techniques that can be used for storing 3D objects whilerequiring considerably less storage space on the storage. Surfacegeometry is often modeled with irregular triangle meshes. The process ofremeshing refers to approximating such geometry using a mesh with(semi)-regular connectivity.

Xiangfeng Gu, Steven Gortler and Hugues Hoppe (Geometry images. InProceedings of the 29th annual conference on Computer graphics andinteractive techniques, pages 355-361. ACM Press, 2002) introduceanother representation called geometry image and a process to convert a3D model a polygonal mesh into an image called geometry image. Ageometry image is a completely regular structure wherein the surface ofthe 3D object is represented by a grid of vertices. Each vertex isconnected to four neighbors except at the grid borders. Hence, ageometry image may be contemplated as a 2D array of vertices, like araster image which is a two-dimensional array of colored pixels. Goingfurther into the comparison, the geometry image may be seen as atwo-dimensional image where each pixel hold in their color channels(red, green, blue) the positions x, y and z of a sampled point on thesurface of the tridimensional object. To serialize a geometry image, oneonly have to store the properties of each vertex (geometry data),because the connectivity is implicit (a vertex is connected to its fourneighbors in the geometry image).

Geometry image representation is sometimes referred to in some onlinevirtual worlds as sculpted prims. Geometry image is notably suitable forthis kind of application due to the ease to operate with it (modeling)and the efficiency to compress and transfer it over the network. Thisrepresentation is also recognized by some modelers.

The process to convert a polygonal mesh into a geometry image is calledremeshing. It consists in finding a convenient 2D parameterization forthe object surface that is represented by a polygonal mesh and then insampling new points on this surface regularly spaced in the 2Dparameterization space. According to the building process, these newpoints form a regular grid, which is the geometry image representation.Consequences of the remeshing process are:

-   -   there is no guarantee that the new sampled points match with        those of the initial polygonal mesh, and it almost never        happens;    -   connectivity data of the initial mesh is completely lost, and        there is no way to know how initial vertices were connected by        looking at the resulting geometry image; and    -   depending on the 2D parameterization and the distance between        two sampled points, some details in the initial polygonal mesh        can disappear in the resulting geometry image. Said otherwise,        the surface made by joining the regularly sampled points may        slightly differ from the original surface due to the building        process. This effect can be attenuated if the number of sampling        points is increased, but this also increases the size of the        geometry image.

Another limitation is that models which are not watertight, which havehigh topology genus or which are not manifold, can require additionalcalculations to find a convenient 2D parameterization at the beginningof the process. This can lead to the need of much more vertices in thegeometry image than in the initial polygonal mesh to describe correctlythe same surface. In the worse situation, this can even lead to theinability to find a solution.

To sum up, the process of remeshing is irreversible in the sense it isnot possible recover the initial polygonal mesh from the geometry image.At the most, the representation obtained from the geometry image is verysimilar to the initial polygonal mesh, but both representations do notnecessarily match in terms of Hausdorff distance. In addition, thegeometry image represents a surface close to the initial mesh but alwayswith few errors: loss of small details, distortions. Furthermore,non-watertight initial mesh can lead to a geometry image that needs moredata for describing the object than the polygonal mesh.

Within this context, there is still a need for an improved compressionmethod which is lossless and completely reversible, and that is suitableto efficiently reduce the storage size of a CAD file.

SUMMARY OF THE INVENTION

According to one aspect, the invention therefore provides acomputer-implemented method for compressing a three-dimensional modeledobject. The method comprises:

-   -   providing a mesh of the three-dimensional modeled object;    -   parameterizing (u,v) the mesh in a two-dimensional plane, the        parameterization of the mesh resulting in a set of vertices        having two-dimensional coordinates;    -   providing a grid on the two-dimensional plane; and    -   modifying the two-dimensional coordinates of each vertex by        assigning one vertex to one intersection of the grid.

The method may comprise one or more of the following:

-   -   after providing the mesh of the three-dimensional modeled        object: storing connectivity data of the mesh of the        three-dimensional modeled object;    -   assigning one vertex to one intersection of the grid is        performed by a repulsion technique that pushes each vertex away        from another;    -   the repulsion technique comprises comparing the distance between        two vertices with the length of the grid cell diagonal; and        pushing the two vertices away if the distance between the two is        lower than the length (L);    -   several iterations of the repulsion technique are performed        until there is at most only one vertex between four        intersections of the grid;    -   after performing a repulsion technique, performing a relaxation        technique that eliminates empty intersections between vertices;    -   the size of the grid is extendable;    -   the set of vertices having modified two-dimensional coordinates        forms a raster image, wherein each vertex of the set is a pixel        of the raster image and the coordinate (x, y, z) of each vertex        of the set is stored in the color channels red/blue/green of the        raster image;    -   supplementary properties of the vertices of the set are stored        in additional color channels;    -   the raster image is reframed for reducing the size of the raster        image;    -   applying on the set of vertices having modified two-dimensional        coordinates one of the following compression scheme: —a discrete        cosine transform; —a wavelet transformations; and    -   connectivity data of the mesh of the three-dimensional modeled        object is compressed.

The invention further proposes a computer-implemented method foruncompressing a three-dimensional modeled compressed according to theabove method. The method comprises:

-   -   providing the set of vertices having modified two-dimensional        coordinates;    -   extracting the vertices from the provided set of vertices; and    -   connecting the vertices with connectivity data.

The invention further proposes a computer-aided design systemcomprising:

-   -   a database storing a mesh of a three-dimensional modeled object;        and    -   means for compressing three-dimensional modeled object according        to the above compression method and/or for decompressing a        three-dimensional modeled according to the above decompression        method.

The invention further proposes a computer program or computer programproduct comprising instructions for execution by a computer, theinstructions comprising means for performing the above compressionmethod and/or decompression method.

The invention further proposes a computer readable storage medium havingrecorded thereon the above computer program.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing will be apparent from the following more particulardescription of example embodiments of the invention, as illustrated inthe accompanying drawings in which like reference characters refer tothe same parts throughout the different views. The drawings are notnecessarily to scale, emphasis instead being placed upon illustratingembodiments of the present invention.

Embodiments of the invention will now be described, by way ofnon-limiting example, and in reference to the accompanying drawings,where:

FIG. 1 shows a flowchart of an example of the method;

FIG. 2 shows an example of a sampling used in the prior art;

FIG. 3 shows an example of snapping one vertex with one intersection;

FIG. 4 shows an example of a polygonal mesh to be remeshed according tothe invention;

FIG. 5 shows an example of vertices of the polygonal mesh of FIG. 4 thatare parameterized (u, v) in a two-dimensional plane;

FIG. 6 shows an example of a regular grid provided in the (u, v) planeof FIG. 5;

FIG. 7 shows an example of vertices of FIG. 5 snapped to theintersections of the regular grid of FIG. 6;

FIGS. 8 to 10 show an example of a repulsion technique that pushes eachvertex away from another;

FIGS. 11 and 12 show an example of a relaxation technique thateliminates empty cells between vertices;

FIG. 13 shows an example of a graphical user interface of CAD system;and

FIG. 14 shows an example of a CAD system.

DETAILED DESCRIPTION OF THE INVENTION

A description of example embodiments of the invention follows.

The teachings of all patents, published applications and referencescited herein are incorporated by reference in their entirety.

With reference to the flowchart of FIG. 1, it is proposed acomputer-implemented method for compressing a three-dimensional (3D)modeled object. The method comprises providing a mesh of thethree-dimensional modeled object. Then, the mesh is parameterized (u,v)in a two-dimensional (2D) plane. It results from the parameterization ofthe mesh a set of vertices having 2D coordinates. Next, a grid isprovided on the two-dimensional plane. Then, the 2D coordinates of eachvertex are modified. The modification of the 2D coordinates is performedby assigning one vertex to one intersection of the grid.

Such a method slightly modifies the definition of a geometry imagedisclosed in Xianfeng Gu, Steven J. Gortler, and Hugues Hoppe (Geometryimages. In Proceedings of the 29th annual conference on Computergraphics and interactive techniques, pages 355-361. ACM Press, 2002) andprovides an improved conversion of a polygonal mesh into 2D imagerepresentation. That is, the present method improves the compression ofa 3D modeled object.

For the sake of explanation, it is reminded that a geometry image, asknown in the art, is obtained from a transformation of an arbitrarysurface of a 3D modeled object onto static mesh as a 2D image, which isa completely regular remesh of the original geometry of the 3D modeledobject, and that support reverse transformation. The geometry imageprovides a completely regular structure that captures geometry as asimple 2D array of quantized points. Surface signals like normals andcolors are stored in similar 2D arrays using the same implicit surfaceparameterization—texture coordinates are absent.

The result of the present method is a two-dimensional array of verticeswhich lie on the surface of the 3D object, but instead of sampling newpoints on the surface of the object at regular interval to get a grid ofpoints, the original vertices are kept from the triangular mesh. Thisadvantageously provides that any vertex hold by the two-dimensionalarray of vertices matches exactly a vertex from the initial polygonalmesh. Reciprocally, any vertex from the initial polygonal mesh matchesexactly a vertex of the geometry image. Hence, it results that anyvertex of the two-dimensional array of vertices has one exactcorresponding vertex in the polygonal mesh, and therefore the process toconvert a polygonal mesh into a geometry image is completely reversible.This involves that a 3D modeled object compressed with the presentmethod can be uncompressed without losing small details as theconversion is lossless. In fact, any detail of the initial polygonalmesh can disappear in the resulting two-dimensional array of verticesbecause the present method of compression does not rely on a sampling ofthe parameterized mesh. By this way, there is no need to increase thenumber of sampling points, which increases the size of the geometryimage. Hence, the present invention advantageously allow to improvecompression rate of a mesh of 3D modeled object that contains detailsthat would be lost using geometry image disclosed in Xianfeng Gu, StevenJ. Gortler, and Hugues Hoppe. In addition, any 3D modeled object mayconverted because the present method does not require any condition onthe closure or on the topology of the mesh of the 3D modeled object.Further advantages of the present invention will appear in thedescription.

The method is computer-implemented. This means that the steps (orsubstantially all the steps) of the method are executed by at least onecomputer. In examples, the triggering of at least some of the steps ofthe method may be performed through user-computer interaction. The levelof user-computer interaction required may depend on the level ofautomatism foreseen and put in balance with the need to implement theuser's wishes. In examples, this level may be user-defined and/orpre-defined.

For instance, the step of providing a mesh of the 3D modeled object maybe performed upon user action. For instance, the user may select a 3Dmodeled object into a dedicated menu or in a feature tree, e.g. the data2500 in FIG.

A typical example of computer-implementation of the method is to performthe method with a system (e.g. a CAD system) comprising a memory storing3D modeled objects, or at least meshes of 3D modeled objects. Thememory, which stores a database, is merely any hardware suitable forsuch storage. The system may further comprise a graphical user interface(GUI). The GUI is coupled with a memory and a processor. The GUI may beadapted for displaying the provided mesh of the 3D modeled object. Thesystem further comprises means for compressing three-dimensional modeledobject according to the above method. The system may further comprisemeans for decompressing a three-dimensional modeled compressed accordingto the above method. Such a system allows the modeling of 3D modeledobjects with low memory resources. Indeed, as the system compresses the3D modeled object according to the efficient compressing methodpresented above, more objects may be stored under compressed form in thedatabase of the system as compared to other systems. In addition, such asystem improves the overall process of designing because detailed 3Dmodeled objects may be compressed without losing information whenuncompressing said compressed 3D modeled object.

The graphical user interface may allow a user to command the compressingof data modeling an object or the decompressing of data modeling anobject. The object may be a part, thus modeled by a CAD file. The systemmay thus store CAD files under compressed form, and decompress them whena designer needs to work on the part, for example by means of thegraphical user interface.

By “database”, it is meant any collection of data (i.e. information)organized for search and retrieval. When stored on a memory, thedatabase allows a rapid search and retrieval by a computer. Databasesare indeed structured to facilitate storage, retrieval, modification,and deletion of data in conjunction with various data-processingoperations. The database may consist of a file or set of files that canbe broken down into records, each of which consists of one or morefields. Fields are the basic units of data storage. Users may retrievedata primarily through queries. Using keywords and sorting commands,users can rapidly search, rearrange, group, and select the field in manyrecords to retrieve or create reports on particular aggregates of dataaccording to the rules of the database management system being used.

In the case of the method, the database can store data representative of3D modeled objects, or at least meshes of 3D modeled objects.

The method generally manipulates meshes of 3D modeled objects. A modeledobject is any object defined by data stored in the database. Byextension, the expression “modeled object” designates the data itself.According to the type of the system, the modeled objects may be definedby different kinds of data.

The system may indeed be any combination of a CAD system, a CAE system,a CAM system, a PDM and/or a PLM system. In those different systems,modeled objects are defined by corresponding data. One may accordinglyspeak of CAD object, PLM object, CAE object, CAM object, CAD data, PLMdata, CAM data, CAE data. However, these systems are not exclusive oneof the other, as a modeled object may be defined by data correspondingto any combination of these systems. A system may thus well be both aCAD and PLM system, as will be apparent from the definitions of suchsystems provided below.

By CAD system, it is meant any system suitable at least for designing amodeled object on the basis of a graphical representation of the modeledobject, such as CATIA. In this case, the data defining a modeled objectcomprise data allowing the representation of the modeled object. A CADsystem may for example provide a representation of CAD modeled objectsusing edges or lines, in certain cases with faces or surfaces. Lines,edges, or surfaces may be represented in various manners, e.g.non-uniform rational B-splines (NURBS). Specifically, a CAD filecontains specifications, from which geometry may be generated, which inturn allows for a representation to be generated. Specifications of amodeled object may be stored in a single CAD file or multiple ones. Thetypical size of a file representing a modeled object in a CAD system isin the range of one Megabyte per part. And a modeled object maytypically be an assembly of thousands of parts.

In the context of CAD, a modeled object may typically be a 3D modeledobject, e.g. representing a product such as a part or an assembly ofparts, or possibly an assembly of products. By product it is meant anitem to be physically manufactured. By “3D modeled object”, it is meantany object which is modeled by data allowing its 3D representation. A 3Drepresentation allows the viewing of the part from all angles. Forexample, a 3D modeled object, when 3D represented, may be handled andturned around any of its axes, or around any axis in the screen on whichthe representation is displayed. This notably excludes 2D icons, whichare not 3D modeled. The display of a 3D representation facilitatesdesign (i.e. increases the speed at which designers statisticallyaccomplish their task). This speeds up the manufacturing process in theindustry, as the design of the products is part of the manufacturingprocess.

A CAD system may be history-based. In this case, a modeled object isfurther defined by data comprising a history of geometrical features. Amodeled object may indeed be designed by a physical person (i.e. thedesigner/user) using standard modeling features (e.g. extrude, revolute,cut, and/or round etc.) and/or standard surfacing features (e.g. sweep,blend, loft, fill, deform, smoothing and/or etc.). Many CAD systemssupporting such modeling functions are history-based system. This meansthat the creation history of design features is typically saved throughan acyclic data flow linking the said geometrical features togetherthrough input and output links. The history based modeling paradigm iswell known since the beginning of the 80's. A modeled object isdescribed by two persistent data representations: history and B-rep(i.e. boundary representation). The B-rep is the result of thecomputations defined in the history. The shape of the part displayed onthe screen of the computer when the modeled object is represented is (atessellation of) the B-rep. The history of the part is the designintent. Basically, the history gathers the information on the operationswhich the modeled object has undergone. The B-rep may be saved togetherwith the history, to make it easier to display complex parts. Thehistory may be saved together with the B-rep in order to allow designchanges of the part according to the design intent. In practice, (B-rep)of parts are the means of describing the geometrical model to themesher, the mesher outputting the mesh displayed.

By CAE (Computer-Aided Engineering) solution, it is meant any solution,software or hardware, suitable for the analysis of the physical behaviorof modeled object. A well-known and widely used CAE technique is theFinite Element Method (FEM) which typically involves a division of amodeled objet into elements which physical behaviors can be computed andsimulated through equations. Such CAE solutions are provided by DassaultSystèmes under the trademark SIMULIA®. Another growing CAE techniqueinvolves the modeling and analysis of complex systems composed aplurality components from different fields of physics without CADgeometry data. CAE solutions allows the simulation and thus theoptimization, the improvement and the validation of products tomanufacture. Such CAE solutions are provided by Dassault Systèmes underthe trademark DYMOLA®.

By CAM (Computer-Aided Manufacturing) solution, it is meant anysolution, software or hardware, suitable for managing the manufacturingdata of a product. The manufacturing data generally includes datarelated to the product to manufacture, the manufacturing process and therequired resources. A CAM solution is used to plan and optimize thewhole manufacturing process of a product. For instance, it can providethe CAM users with information on the feasibility, the duration of amanufacturing process or the number of resources, such as specificrobots, that may be used at a specific step of the manufacturingprocess; and thus allowing decision on management or requiredinvestment. CAM is a subsequent process after a CAD process andpotential CAE process. Such CAM solutions are provided by DassaultSystèmes under the trademark DELMIA®.

By PDM (Product Data Management) solution, it is meant any solution,software or hardware, suitable for managing all types of data related toa particular product. A PDM solution may be used by all actors involvedin the lifecycle of a product: primarily engineers but also includingproject managers, finance people, sales people and buyers. A PDMsolution is generally based on a product-oriented database. It allowsthe actors to share consistent data on their products and thereforeprevents actors from using divergent data. Such PDM solutions areprovided by Dassault Systèmes under the trademark ENOVIA™.

FIG. 13 shows an example of the GUI of the system, wherein the system isa CAD system.

The GUI 2100 may be a typical CAD-like interface, having standard menubars 2110, 2120, as well as bottom and side toolbars 2140, 2150. Suchmenu- and toolbars contain a set of user-selectable icons, each iconbeing associated with one or more operations or functions, as known inthe art. Some of these icons are associated with software tools, adaptedfor editing and/or working on the 3D modeled object 2000 displayed inthe GUI 2100. The software tools may be grouped into workbenches. Eachworkbench comprises a subset of software tools. In particular, one ofthe workbenches is an edition workbench, suitable for editinggeometrical features of the modeled product 2000. In operation, adesigner may for example pre-select a part of the object 2000 and theninitiate an operation (e.g. change the dimension, color, etc.) or editgeometrical constraints by selecting an appropriate icon. For example,typical CAD operations are the modeling of the punching or the foldingof the 3D modeled object displayed on the screen.

The GUI may for example display data 2500 related to the displayedproduct 2000. In the example of FIG. 2, the data 2500, displayed as a“feature tree”, and their 3D representation 2000 pertain to a brakeassembly including brake caliper and disc. The GUI may further showvarious types of graphic tools 2130, 2070, 2080 for example forfacilitating 3D orientation of the object, for triggering a simulationof an operation of an edited product or render various attributes of thedisplayed product 2000. A cursor 2060 may be controlled by a hapticdevice to allow the user to interact with the graphic tools.

FIG. 14 shows a computer system, e.g. a CAD system.

The client computer comprises a central processing unit (CPU) 1010connected to an internal communication BUS 1000, a random access memory(RAM) 1070 also connected to the BUS. The client computer is furtherprovided with a graphical processing unit (GPU) 1110 which is associatedwith a video random access memory 1100 connected to the BUS. Video RAM1100 is also known in the art as frame buffer. A mass storage devicecontroller 1020 manages accesses to a mass memory device, such as harddrive 1030. Mass memory devices suitable for tangibly embodying computerprogram instructions and data include all forms of nonvolatile memory,including by way of example semiconductor memory devices, such as EPROM,EEPROM, and flash memory devices; magnetic disks such as internal harddisks and removable disks; magneto-optical disks; and CD-ROM disks 1040.Any of the foregoing may be supplemented by, or incorporated in,specially designed ASICs (application-specific integrated circuits). Anetwork adapter 1050 manages accesses to a network 1060. The clientcomputer may also include a haptic device 1090 such as cursor controldevice, a keyboard or the like. A cursor control device is used in theclient computer to permit the user to selectively position a cursor atany desired location on display 1080, as mentioned with reference toFIG. 13. In addition, the cursor control device allows the user toselect various commands, and input control signals. The cursor controldevice includes a number of signal generation devices for input controlsignals to system. Typically, a cursor control device may be a mouse,the button of the mouse being used to generate the signals. As anotherexample, the display 1080 may be a sensitive touch display, and thecursor control may be performed upon user action (e.g. touch) on thetouch sensitive display.

A computer program may comprise instructions by a computer, theinstructions comprising means for causing the above system to performthe above method. The invention may for example be implemented indigital electronic circuitry, or in computer hardware, firmware,software, or in combinations of them. Apparatus of the invention may beimplemented in a computer program product tangibly embodied in amachine-readable storage device for execution by a programmableprocessor; and method steps of the invention may be performed by aprogrammable processor executing a program of instructions to performfunctions of the invention by operating on input data and generatingoutput.

The invention may advantageously be implemented in one or more computerprograms that are executable on a programmable system including at leastone programmable processor coupled to receive data and instructionsfrom, and to transmit data and instructions to, a data storage system,at least one input device, and at least one output device. Theapplication program may be implemented in a high-level procedural orobject-oriented programming language, or in assembly or machine languageif desired; and in any case, the language may be a compiled orinterpreted language.

Referring back to FIG. 1, it is now discussed an example of the methodof the present invention.

At step S10, it is provided a mesh of 3D modeled object. This may beperformed upon user action, e.g. the user selects a 3D modeled objectthat may be stored on a memory. This may also be automatically achievedby the computer system performing the method. Providing means that themesh of the 3D modeled object is available to the computer system, thatis, the system can access data relative to the mesh. Typically, thecomputer system may display the mesh of the 3D modeled object once it isavailable to the system, as presented for instance on FIG. 4 that showsthe mesh of a 3D modeled object modeling a statue.

Then, at step S20, connectivity data of the mesh is stored. Forinstance, the connectivity data may be stored on the memory that storesthe 3D mesh. Connectivity data comprise the indices of the verticesjoined by each polygon of the mesh. Connectivity data thus identify, foreach vertex of the mesh, the neighbor vertex (or vertices) that areconnected to said each vertex of the mesh. Keeping connectivity data ofthe polygonal mesh advantageously facilitates the identification of thevertices which are close on the surface of the object because verticesare now not necessary close in the two-dimensional array, as explainedbelow.

It is to be understood that the step S20 can be optional because thepolygonal mesh provided at step S10 may be already divided into geometrydata and connectivity data. Hence, in this case, the memory stores bothgeometry data and connectivity data, and therefore, connectivity data isavailable for further steps.

Next, at step S30, the mesh of the provided 3D modeled object isparameterized (u, v) in a two-dimensional plane. Parameterizing the meshin a two-dimensional plane means that it is determined the parametersnecessary for having a specification of the 3D modeled object in a 2Dspace. In practice, the parameterization comprises the identification ofa complete set of effective coordinates (u, v) of each vertex of themesh in the 2D plane. Parameterization is performed as known in the art,e.g. ABF++ parameterization algorithm may be used. For example this canbe done so that the whole mesh may be unfold in the two-dimensionalplane with less distortion or so that the mesh cut into a small numberof charts may be unfold in the two-dimensional plane with lessdistortion.

FIG. 5 shows the mesh of FIG. 4 that have been parameterized in a 2Dplane. The parameterization of the mesh results in a set of verticeshaving two-dimensional coordinates (u,v) in a 2D plane. Interestingly,each vertex of the original mesh of the 3D modeled object is representedby one vertex in the 2D plane.

Referring back to FIG. 1, at step S40, a grid is provided on the 2Dplane. In practice, the grid is automatically provided, e.g. by thecomputer system. Providing a grid on the 2D plane means that a set oflines that cross each other is defined on the 2D plane. The linesintersect, thus providing a set of intersections on the 2D planes. Inpractice, the lines are uniformly spaced horizontal and perpendicularlines, so that the intersections are regularly placed on the 2D plane.This advantageously allows improving the construction of atwo-dimensional array as it will be depicted in the following steps. Itis to be understood that any configuration of the lines may be used.

The number of intersections of the grid is at least equal to the numberof vertices of the parameterized mesh. In practice, the number ofintersections is slightly bigger than the number of vertices of themesh.

Interestingly, the size of the grid may be extendable. Extending thegrid means that the number of lines that cross each other can beincreased, thus increasing the number of intersections of the grid. Inpractice, the extension of the grid is performed by adding new lines atthe edges of the grid. Said otherwise, the density of vertices of thegrid is not increased. Inversely, the size of the grid may be shorten,that is, one or more lines of the grid may be removed.

In practice, the step S40 may be performed before the parameterizationof the mesh of the 3D modeled object is done. Typically, the grid isadded on the 2D plane, and then the parameterization is carried out.Then, after that the parameterization of the mesh has occurred, the sizeof the grid may be dynamically changed (e.g. extended) in response tothe result of the parameterization: indeed, it generally results fromthe parameterization of the mesh a non-uniform distribution of theresulting set of vertices. For instance, lines may be added on the edgeof the grid close to a zone of the 2D plane wherein the density ofvertices of the parameterized mesh is the most important. This mayadvantageously improve the efficiency of the further next S50.

Each intersection on the 2D plane has also a coordinate (u, v) in the 2Dplane. The coordinate of the intersection may be defined by using thesame referential than the one used at the parameterization step of themesh.

FIG. 6 shows the parameterized 2D plane of FIG. 5 on which a grid hasbeen added. In this example, the number of uniformly spaced horizontaland perpendicular lines has be selected so that the number ofintersection is a bit larger than the number of vertices of theparameterized mesh.

Next, at step S50, the two-dimensional coordinates (u, v) of each vertexis modified. The modification is done by assigning one vertex to oneintersection of the grid. This means that only one vertex can be placedon one intersection. Hence, two vertices cannot be assigned to oneintersection. Assigning one vertex to one intersection may be calledsnapping: one intersection acts as a snap for one vertex.

Assigning means that one vertex is attached to one intersection, andthis is performed by replacing the coordinate in the 2D plane of thevertex by the coordinate in the 2D plane of the intersection.

It is to be understood that a vertex of the parameterized mesh may haveidentical coordinate as an intersection before the step S50 isperformed. In this case, the vertex's coordinate are kept unchanged.

At the end of the step S50, a grid in the 2D plane is obtained where anyvertex of the initial mesh is assigned to a one different intersection.The grid is therefore equivalent to a 2D array of vertices.

Referring now to FIG. 3, it is shown an example of snapping. Each one ofthe three vertices of a parameterized mesh (having here the shape of atriangle 30) is assigned to one intersection 32, 34, 36. Themodification of the coordinates of each vertex may be contemplated as adisplacement of said vertices, which is represented by arrows.

Interestingly, even if the parameterized mesh is small (for instance thetriangle 38 that represents a small detail of the original 3D modeledobject), the modification of the coordinates of the triangle 38 will beperformed any, in as similar way as for the triangle 30. Hence, nodetail of the initial polygonal mesh can disappear in the resultingtwo-dimensional array of vertices because the present method ofcompression does not rely on a sampling of the parameterized mesh of theprior art. Such a sampling method is shown on FIG. 2: the triangle 20 issampled several times (represented by the black dots), while the smalltriangle 22 is not sampled because the sampling interval is too large.Hence, small details are lost.

In addition, the present invention decreases the quantity of data to bestored because only coordinates of the intersection on which verticesare assigned are to be kept in memory. On the contrary, sampling basedmethod requires to store more points.

FIG. 7 shows the result of the modification of the 2D coordinates (u, v)of each vertex after that each vertex has been assigned to one differentintersection of the grid. The vertices of the parameterized mesh havebeen reordered in such a way that a two-dimensional array is now formed.

Each vertex of the parameterized mesh has a coordinate (u, v) in theparameterization space, and so do the intersection of the grid. In thisparameterization space some vertices may be concentrated in a specificarea (more than 1 vertex between 4 intersections of the grid), leavingother regions of the grid with fewer vertices. Especially, theconcentration may be problematic when there is more than one vertex percell of the grid, a cell being the area comprised between 4intersections of the grid. On the contrary, the some part of the 2Dplane may have a smaller density of vertex (less than 1 vertex between 4intersections of the grid). It is reminded that the number of gridintersections has been chosen to be close (and slightly bigger) than thenumber of vertices.

FIG. 8 shows a grid wherein the number of vertex (or vertices) on eachcell of the grid varies.

To be able to assign easily one vertex to one intersection of the grid,a modification of vertex (u, v) coordinates may be required so thatthere is no more than one vertex between four intersections, that is, nomore than one vertex per cell of the grid. If this condition isrespected, then it is possible to assign each vertex to one of the fourintersections that define a cell of the grid.

In the event a vertex is located on the frontier between two cells,(that is, the vertex is placed on the common edge connecting two commonintersections of two cells), the decision to assign the vertex to one orthe other of the two cells may be performed according to a predeterminedrule. For instance, the rule may decide that the vertex located on thefrontier is assigned to the cell having less vertices.

In the event a vertex is already located on an intersection of the grid,the 2D coordinate of the vertex is the same as the coordinate of theintersection, and the vertex is not moved in this case. Said otherwise,the 2D coordinate of a vertex located on an intersection is not modifiedwhen the step S50 is carried out.

FIG. 9 illustrates the coordinates (u, v) of the vertices shown in FIG.8 that have been modified so that there is only one vertex between fourintersections of the grid. Therefore, each vertex of each cell of thegrid can be assigned to the upper left intersection (amongst the 4circling it). Hence, it is guaranteed that each vertex is assigned to adifferent intersection, as illustrated on FIG. 10.

Referring now to FIG. 1, it is now discussed an example of theattribution of one vertex to one intersection of the grid, the 2Dcoordinates of each vertex being modified as a result. In this example,one vertex is assigned to one intersection of the grid using a repulsiontechnique that pushes each vertex away from another in accordance with acriterion. The repulsion technique relies on a particle repulsion thatsimulates repulsion forces between vertices in the parameterizationspace. The criterion may be related to the force.

At step S500, the distance (D_(Vx, Vy)) between two vertices, namely Vxand Vy, is compared with the length (L) of the grid cell diagonal. Oneunderstands that the lines forming the grid are uniformly spacedhorizontal and perpendicular lines, so that the intersections areregularly placed on the 2D plane and all the cells of the grid has asame cell diagonal length (L).

The term distance means a numerical description of how far apartvertices. The distance may be typically an Euclidien distance. Othertypes of distance may be used such as Manhattan distance or Chebyshevdistance. A cell of the grid is the area comprised between 4intersections of the grid.

In the event the evaluated distance between the two vertices is lowerthan the length (L) of the grid cell diagonal, the two vertices arepushed away from another, at step 520. The distance that is applied forpushing away two vertices may be defined as follows. A vertex noted Ahas n vertices B_(i) in its neighborhood with distances d_(i) that arelower than the length (L) of the grid cell diagonals. Each vertex B_(i)adds a contribution c_(i) for pushing away the point A. The contributionis defined by the relation c_(i)=(L−d_(i))×u_(i), wherein u_(i) is aunit vector providing a direction from B to A, that is, the directionwith which the vertex A is pushed away from the vertex B_(i). The vertexA pushed away of the vertex B with a distance M=λ×η×Σ_(i=0) ^(n) c_(i),wherein:

-   -   λ is a factor initiated at 0 and progressively increasing to 1        for each iteration. The factor λ advantageously provides a        stability of the algorithm and avoids a dispersal of the        vertices;    -   η is a factor that limits the size of M in the event Σ_(i=0)        ^(n) c_(i) is too large. η advantageously avoids that one vertex        jumps in one iteration from a cell to another one that is too        far.

In the event the distance between the two vertices is greater than thelength (L) of the grid cell diagonal, the two vertices are not spaced.

Several iterations of the repulsion technique are performed until thereis at most only one vertex between four intersections of the grid, thatis, one vertex per cell. This means that, for a given vertex, it ischecked whether the distance with its neighbor(s) is larger than thelength (L). In practice, the neighbors are selected in the cell whereinthe vertex is located, and then the distance checking is carried out forvertices that are in cells surrounding the cell wherein the vertex islocated. The cells surrounding a cell are the cells that share a commonedge with this cell.

An example of a pseudo-algorithm for scanning the distance between thevertices of the cells and moving the vertices follows:

While there exists cells comprising two or more vertices    {    Foreach cell of the grid       {       For each vertex A in the cell         {          If there exists a vertex B in the same cell or in aneighbor cell of          the cell wherein the vertex is located with adistance from A < L             {             The contribution providedby B to push away A is             registered; this is noted as being acollision between A and             B;             }          }       }   According to the number of collisions discovered and the number ofiterations of    this algorithm, the value of λ is increased toward thevalue 1    For each vertex A involved in a collision    {    The valueof the distance M is computed    The vetex A is moved of M in the 2Dplane (possibly, and this is what is looking    for, the vertex Achanges of cell    If vertices are out of the grid as a consequence oftheir displacement, the size of    the grid is increase (for instance byadding lines and rows at the edges of the grid)    } }

Hence, at step S530, one vertex of the parameterized mesh has beenassigned to on intersection of the grid using the repulsion techniqueperformed using iteration. Iterations of the repulsion technique areperformed until there is at most only one vertex between fourintersections of the grid. The iteration advantageously allows to reducethe overall number of comparison to be performed is limited. Inaddition, the iteration guarantees that there is at most only one vertexbetween four grid intersections, and two vertices that were close beforethat step in the parameterization space are still close now: they areonly separated by cells containing vertex that were in between them orcells containing no vertex.

As discussed in reference to step S40, the size of the grid may bedynamically changed (e.g. extended). It may be changed in response tothe result of the repulsion technique: indeed, it generally results fromthe repulsion technique that points near the edge of the grid are pushedaway outside the grid. In this case, new lines may be added on the edgeof the grid close so that the pushed vertex (vertices) is alwayscomprised between four intersections of the grid. As another example,the grid may have a hidden margin that comprises one or moreintersections: the hidden intersections are unhidden and pushed awayvertices can be assigned to the unhidden intersections.

At the end of step S50, the 2D coordinates of all the vertices of theparameterized mesh of the 3D modeled have been modified by assigning onevertex of the parameterized mesh to one intersection of the grid. A 2Darray of vertices has obtained as a result of steps S10 to S50. Thearray contains vertices which were all in the initial polygonal mesh ofthe 3d modeled object. This array is equivalent to the initial polygonalmesh if the initial connectivity data to it. With the array and theconnectivity data, it is possible to get back the initial polygonalmesh. The remeshing process is therefore a completely reversibleprocess.

At step S60, empty intersections between vertices are eliminated. Anempty intersection is an intersection that does not comprise any vertex.The elimination of empty intersection may be performed using arelaxation technique, as illustrated on FIGS. 11 and 12.

The relaxation step is typically performed after the particle repulsionstep S500-S530. This relaxation step may use seem carving that is methodorigination from image processing. Seam carving is an algorithm forimage resizing: it functions by establishing a number of seams that arepaths of least importance in the 2D array of vertices. The algorithmautomatically removes seams, and thus advantageously reduces size of the2D array of vertices. Seam carving may also allow manually definingareas in which pixels may not be modified.

Seem carving iteratively removes seams of empty grid intersections ofthe 2D array so that vertices which are close on the object model andthat were close on the grid before a seam removal stay close after theseam removal.

Referring now on FIG. 11, it is illustrated one iteration of the seamcarving operation wherein a set of empty intersections has beendetermined in the 2D array of vertices obtained as a result of steps S10to S50. White vertices and black vertices are separated by a seam ofempty intersection.

Referring now to FIG. 12, it is illustrated the 2D array of vertices ofFIG. 11 wherein the seam has been removed. The size of the 2D array hastherefore been reduced. It is to be understood that some emptyintersection may still be in the 2D array, even after that all theiterations of the relaxation step have been performed.

It is to be understood that the relaxation step may be performed withany algorithm able to identify empty intersections. Preferably, thealgorithm should be able to maintain close vertices that are close inthe parameterized mesh.

The output of step S60 is thus a 2D array of vertices of theparameterized mesh of the 3D modeled that has a reduced size compared tothe 2D array taken in input.

In both steps S50 and S60, the set of vertices having modified 2Dcoordinates forms a raster image, wherein each vertex of the set is apixel of the raster image and the coordinate (x, y, z) of each vertex ofthe set is stored in the color channels red/green/blue (RGB) of theraster image. Raster image means a dot matrix data structurerepresenting a generally rectangular grid of pixels, e.g. a rectangular2D array of vertices. The RGB color model is an additive color model inwhich red, green, and blue light are added together in various ways toreproduce a broad array of colors, as known in the art.

Interestingly, supplementary vertex properties (like normal per vertex,texture coordinates . . . ) may be stored as well in additional colorchannels. Hence, the raster image can possibly comprises all theproperties of the initial mesh of the 3D modeled, being understood thatthe number of properties stored with each vertex is limited by thenumber of color channels.

Optionally, the raster image may be reframed for reducing the size ofthe raster image. This is performed, as known in the art.

Next, at step S80, a compression scheme is applied on the raster imageand the connectivity data. The compression scheme may be based, but isnot limited to, a discrete cosine transform such as JPEG format, awavelet transformations such JPEG 2000 format. In fact, all thecompression schemes that might be applied on a raster image can be used.Interestingly, since the 2D array of vertices raster image grid has beenbuilt so that vertices close in the grid are usually close on thesurface of the initial object, x, y and z coordinates of adjacentvertices in the 2D array are strongly correlated; thus these compressionschemes will achieve great results.

The connectivity data may be compressed with a compression schemeadapted to the format used for storing information relative toconnectivity data. For instance, connectivity data may be stored in atext file, and the compression scheme may be, but is not limited to, ZIPcompression, RAR compression.

Tools and operations dedicated to image processing (compression, videocompression, watermarking, morphing . . . ) may be applied to theobtained raster image. The overall compression rate of the presentinvention is improved compared to known solution using geometry images,despite the presence of connectivity data. Indeed, less informationneeds to be stored because the remeshing of the present invention isindependent of sampling points a number of sampling points.

A three-dimensional modeled compressed according to the presentinvention can be uncompressed using the following steps.

First, it is provided a set of vertices having modified two-dimensionalcoordinates. For instance, a 2D array of vertices obtained as a resultof step S50 or S60, a raster image obtained as a result of step S70, acompressed raster image of step S80.

Next, the vertices are extracted from the provided set of vertices. Theextraction may be typically performed by identifying the intersectionsof the 2D array. For instance, pixels of the raster image areidentified.

Then, the extracted vertices are connected in accordance withconnectivity data. The extracted vertices are placed in the 3D space.The coordinates of the extracted vertices may be obtained from the colorchannels RGB of the raster image.

The preferred embodiment of the present invention has been described. Itwill be understood that various modifications may be made withoutdeparting from the spirit and scope of the invention. Therefore, otherimplementations are within the scope of the following claims.

While this invention has been particularly shown and described withreferences to example embodiments thereof, it will be understood bythose skilled in the art that various changes in form and details may bemade therein without departing from the scope of the inventionencompassed by the appended claims.

What is claimed is:
 1. A computer-implemented method for compressing athree-dimensional modeled object, comprising: providing a mesh of thethree-dimensional modeled object; parameterizing (u,v) the mesh in atwo-dimensional plane, the parameterization of the mesh resulting in aset of vertices having two-dimensional coordinates; providing a grid onthe two-dimensional plane; and modifying the two-dimensional coordinatesof each vertex by assigning one vertex to one intersection of the grid.2. The computer-implemented method of claim 1, further comprising, afterproviding the mesh of the three-dimensional modeled object: storingconnectivity data of the mesh of the three-dimensional modeled object.3. The computer-implemented method of claim 1, wherein assigning onevertex to one intersection of the grid is performed by a repulsiontechnique that pushes each vertex away from another.
 4. Thecomputer-implemented method of claim 3, wherein the repulsion techniquecomprises: comparing the distance between two vertices with the lengthof the grid cell diagonal; and pushing the two vertices away if thedistance between the two is lower than the length (L).
 5. Thecomputer-implemented method of claim 3, wherein several iterations ofthe repulsion technique are performed until there is at most only onevertex between four intersections of the grid.
 6. Thecomputer-implemented method of claim 3, further comprising, afterperforming the repulsion technique, performing a relaxation techniquethat eliminates empty intersections between vertices.
 7. Thecomputer-implemented method of claim 1, wherein the size of the grid isextendable.
 8. The computer-implemented method of claim 1, wherein theset of vertices having modified two-dimensional coordinates forms araster image, wherein each vertex of the set is a pixel of the rasterimage and the coordinate (x, y, z) of each vertex of the set is storedin the color channels red/blue/green of the raster image.
 9. Thecomputer-implemented method of claim 8, wherein supplementary propertiesof the vertices of the set are stored in additional color channels. 10.The computer-implemented method of claim 8, wherein the raster image isreframed for reducing the size of the raster image.
 11. Thecomputer-implemented method of claim 1, further comprising applying onthe set of vertices having modified two-dimensional coordinates one ofthe following compression schemes: a discrete cosine transform; and awavelet transformation.
 12. The computer-implemented method of claim 11,further comprising: after providing the mesh of the three-dimensionalmodeled object, storing connectivity data of the mesh of thethree-dimensional modeled object, wherein connectivity data of the meshof the three-dimensional modeled object is compressed.
 13. Acomputer-implemented method for uncompressing a three-dimensionalmodeled object compressed according to the method of claim 2, the methodfor uncompressing the three-dimensional modeled object comprising:providing the set of vertices having modified two-dimensionalcoordinates; extracting the vertices from the provided set of vertices;and connecting the vertices with connectivity data.
 14. A computer-aideddesign system comprising: a database storing a mesh of athree-dimensional modeled object; and means for compressing thethree-dimensional modeled object by: providing a mesh of thethree-dimensional modeled object; parameterizing (u,v) the mesh in atwo-dimensional plane, the parameterization of the mesh resulting in aset of vertices having two-dimensional coordinates; providing a grid onthe two-dimensional plane; and modifying the two-dimensional coordinatesof each vertex by assigning one vertex to one intersection of the grid.15. The computer-aided design system as claimed in claim 14 furthercomprising means for storing, after providing the mesh of thethree-dimensional modeled object, the storing means storing connectivitydata of the mesh of the three-dimensional modeled object.
 16. Thecomputer-aided design system as claimed in claim 15 further comprisingmeans for applying on the set of vertices having modifiedtwo-dimensional coordinates one of the following compression schemes: adiscrete cosine transform and a wavelet transformations, whereinconnectivity data of the mesh of the three-dimensional modeled object iscompressed.
 17. The computer-aided design system as claimed in claim 16further comprising means for uncompressing the compressedthree-dimensional modeled object by: providing the set of verticeshaving modified two-dimensional coordinates; extracting the verticesfrom the provided set of vertices; and connecting the vertices withconnectivity data.
 18. The computer-aided design system as claimed inclaim 14, wherein assigning one vertex to one intersection of the gridis performed by a repulsion technique that pushes each vertex away fromanother.
 19. The computer-aided design system as claimed in claim 14,wherein the size of the grid is extendable.
 20. The computer-aideddesign system as claimed in claim 14, wherein the set of vertices havingmodified two-dimensional coordinates forms a raster image, wherein eachvertex of the set is a pixel of the raster image and the coordinate (x,y, z) of each vertex of the set is stored in the color channelsred/blue/green of the raster image.
 21. A computer program productcomprising: a computer-readable medium comprising instructions forexecution by a computer; and the instructions comprising program codecausing the computer to: provide a mesh of a three-dimensional modeledobject of computer-aided design; parameterize (u,v) the mesh in atwo-dimensional plane, the parameterization of the mesh resulting in aset of vertices having two-dimensional coordinates; provide a grid onthe two-dimensional plane; and modify the two-dimensional coordinates ofeach vertex by assigning one vertex to one intersection of the grid.